In general, I'm not a big Chaplin fan, as his films are often a bit too sentimental for my liking. However, I love The Kid (1921), because I adore young Jackie Coogan. He was such a beautiful child and a natural talent. He brought out the best qualities in Chaplin. Also, The Circus (1928) pleasantly surprised me. I liked A Woman of Paris (1923) which Chaplin directed but didn't star in. Chaplin intended it to be a showcase for Edna Purviance, but even though she's great, the story was a bit on the soapy side.
I like the Arbuckle shorts with Keaton, especially Coney Island (1917) and Good Night, Nurse (1918). Guess I just can't resist Roscoe in drag. His dog, Luke, is pretty great, too.
Buster Keaton, to me, is the greatest of the silent comics. I'll mention Sherlock, Jr. (1924) because it was the first of his silents I saw (and that was thanks to a promo at TCM where Woody Allen cited it as an inspiration). Besides the two features TB mentioned, I'd highly recommend The Navigator (1924) and Steamboat Bill, Jr. (1928), but as always, beware of inferior scores. One Week (1920) is probably my favorite short.